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January  2017, 13(1): 349-373. doi: 10.3934/jimo.2016021

Impact of price cap regulation on supply chain contracting between two monopolists

Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

* Corresponding author: Yanfei Lan, Email: lanyf@tju.edu.cn

Received  August 2013 Published  March 2016

This paper considers a supply chain with an unregulated upstream monopolist (she) supplying a kind of products to a regulated downstream monopolist (he). The upstream monopolist's production efficiency, which represents her type, is only privately known to herself. When the downstream monopolist trades with the upstream monopolist, his pricing discretion is constrained by price cap regulation (PCR). We model this problem as a game of adverse selection with the price cap constraint. In this model, the downstream monopolist offers a menu of contracts, each of which consists of two parameters: the transfer payment and the retail price. We show that private information can weaken PCR's impact on the optimal contract, and PCR can dampen the effects of private information. We also shed light on the influences of private information and PCR on the optimal contract, the downstream monopolist's profit, the upstream monopolist's profit, the consumers' surplus and the social total welfare, respectively. Finally, a numerical example is given to illustrate the proposed results.

Citation: Jing Feng, Yanfei Lan, Ruiqing Zhao. Impact of price cap regulation on supply chain contracting between two monopolists. Journal of Industrial and Management Optimization, 2017, 13 (1) : 349-373. doi: 10.3934/jimo.2016021
References:
[1]

M. Armstrong and J. Vickers, Multiproduct price regulation under asymmetric information, J. Ind. Econ., 8 (2000), 137-160.  doi: 10.1111/1467-6451.00115.

[2]

M. Armstrong and J. Vickers, Welfare effects of price discrimination by a regulated monopolist, Rand J. Econ., 22 (1991), 571-580. 

[3]

M. Armstrong and D. Sappington, Recent developments in the theory of regulation, in Handbook of Industrial Organization, Elsevier Science Publishers, (2007), 1557-1700. 

[4]

Armstrong1994 M. Armstrong, S. Cowan and J. Vickers, Regulatory Reform: Economic Analysis and the British Experience, MIT Press, Cambridge, MA, 1994.

[5]

M. Armstrong, Multiproduct nonlinear pricing, Econometrica, 64 (1996), 51-76.  doi: 10.2307/2171924.

[6]

D. Baron and R. Myerson, Regulating a monopolist with unknown costs, Econometrica, 50 (1982), 911-930.  doi: 10.2307/1912769.

[7]

R. Barlow and F. Proschan, Mathematical Theory of Reliability, John Wiley and Sons, New York, 1965.

[8]

M. Bagnoli and T. Bergstrom, Log-concave probability and its applications, Econ. Theor., 26 (2005), 445-469.  doi: 10.1007/s00199-004-0514-4.

[9]

A. BurnetasS. Gilbert and C. Smith, Quantity discount in single period supply contracts with asymmetric demand information, IIE Trans., 39 (2007), 465-479. 

[10]

M. CakanyildirimQ. FengX. Gan and S. Sethi, Contracting and coordination under asymmetric production cost information, Prod. Oper. Manag., 21 (2012), 345-360. 

[11]

G. Cachon, Competitive supply chain inventory management, in Quantitative Models for Supply Chain Management, Kluwer, Boston, MA, 1998, 111–146. doi: 10.1007/978-1-4615-4949-9-5.

[12]

G. Cachon, Supply chain coordination with contracts, in Handbook in Operations Research and Management Science: Supply Chain Management, Elsevier Science Publishers, North Holland, The Netherlands, 2003, 227–339. doi: 10.1016/S0927-0507(03)11006-7.

[13]

G. Cachon and M. Lariviere, Contracting to assure supply: How to share demand forecasts in supply chain, Manage. Sci., 47 (2001), 629-646. 

[14]

J. ChenH. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. 

[15]

C. Corbett and X. Groote, A supplier's optimal quantity discount policy under asymmetric information, Manage. Sci., 46 (2000), 444-450. 

[16]

C. CorbettD. Zhou and C. Tang, Designing supply contracts: Contract type and information asymmetry, Manage. Sci., 50 (2004), 550-559. 

[17]

A. Ha, Supplier-buyer contracting: Asymmetric cost information and cutoff policy for buyer participation, Nav. Res. Log., 48 (2001), 41-64. 

[18]

E. Inssa and F. Stroffolini, Price-cap regulation, revenue sharing and information acquisition, Inf. Econ. Policy, 17 (2005), 217-230. 

[19]

E. Inssa and F. Stroffolini, Price-cap regulation and information acquisition, Int. J. Ind. Organ., 20 (2002), 1013-1036. 

[20]

A. IozziJ. Poritz and E. Valentini, Socal preferences and price cap regualtion, J. Public Econ. Theory, 4 (2002), 95-114. 

[21]

J. KangD. Weisman and M. Zhang, Do consumers benefit from tighter price cap regulation?, Econ. Lett., 67 (2000), 113-119.  doi: 10.1016/S0165-1765(99)00252-9.

[22]

P. Law, Tighter average revenue regulation can reduce consumer welfare, J. Ind. Econ., 43 (1995), 399-404.  doi: 10.2307/2950551.

[23]

J. Laffont and D. Mortimort The Theory of Incentive: The Principal-Agent Model, Princeton University Press, Princeton, NJ, 2002.

[24]

J. Laffont and J. Rochet, Regulation of a risk averse firm, Game. Econ. Behav., 25 (1998), 149-173.  doi: 10.1006/game.1998.0639.

[25]

T. Lewis and C. Garmon, Fundamentals of Incentive Regulation, 12th PURC/World Bank International Training Program on Utility Regulation and Strategy, Gainesville, 2002.

[26]

C. Liston, Price cap versus rate of return regulation, J. Regul. Econ., 5 (1993), 25-48.  doi: 10.1007/BF01066312.

[27]

M. Lariviere, A note on probability distributions with increasing generalized failure rates, Oper. Res., 54 (2006), 602-604.  doi: 10.1287/opre.1060.0282.

[28]

R. Myerson, Incentive compatibiltiy and the bargaining problem, Econometrica, 47 (1979), 61-74.  doi: 10.2307/1912346.

[29]

Ö. Özer and W. Wei, Strategic commitment for optimal capacity decision under asymmetric forecast information, Manage. Sci., 52 (2006), 1238-1257. 

[30]

Ö. Özer and G. Raz, Supply chain sourcing under asymmetric information, Prod. Oper. Manag., 20 (2011), 92-115. 

[31]

J. Reitzes, Downstream price-cap regulation and upstream market power, J. Regul. Econ., 33 (2008), 179-200. 

[32]

D. Sappington and D. Weisman, Price cap regulation: What have we learned from 25 years of experience in the telecommunications industry?, J. Regul. Econ., 38 (2010), 227-257. 

[33]

Y. Shen and S. Willems, Coordinating a channel with asymmetric cost information and the manufactures' optimality, Int. J. Prod. Econ., 135 (2012), 125-135. 

[34]

D. Sibley, Asymmetric information, incentives and price cap regulation, Rand J. Econ., 20 (1989), 392-404.  doi: 10.2307/2555578.

[35]

G. Voigt and K. Inderfurth, Supply chain coordination and setup cost reduction in case of asymmetric information, OR Spectrum, 33 (2011), 99-122. 

show all references

References:
[1]

M. Armstrong and J. Vickers, Multiproduct price regulation under asymmetric information, J. Ind. Econ., 8 (2000), 137-160.  doi: 10.1111/1467-6451.00115.

[2]

M. Armstrong and J. Vickers, Welfare effects of price discrimination by a regulated monopolist, Rand J. Econ., 22 (1991), 571-580. 

[3]

M. Armstrong and D. Sappington, Recent developments in the theory of regulation, in Handbook of Industrial Organization, Elsevier Science Publishers, (2007), 1557-1700. 

[4]

Armstrong1994 M. Armstrong, S. Cowan and J. Vickers, Regulatory Reform: Economic Analysis and the British Experience, MIT Press, Cambridge, MA, 1994.

[5]

M. Armstrong, Multiproduct nonlinear pricing, Econometrica, 64 (1996), 51-76.  doi: 10.2307/2171924.

[6]

D. Baron and R. Myerson, Regulating a monopolist with unknown costs, Econometrica, 50 (1982), 911-930.  doi: 10.2307/1912769.

[7]

R. Barlow and F. Proschan, Mathematical Theory of Reliability, John Wiley and Sons, New York, 1965.

[8]

M. Bagnoli and T. Bergstrom, Log-concave probability and its applications, Econ. Theor., 26 (2005), 445-469.  doi: 10.1007/s00199-004-0514-4.

[9]

A. BurnetasS. Gilbert and C. Smith, Quantity discount in single period supply contracts with asymmetric demand information, IIE Trans., 39 (2007), 465-479. 

[10]

M. CakanyildirimQ. FengX. Gan and S. Sethi, Contracting and coordination under asymmetric production cost information, Prod. Oper. Manag., 21 (2012), 345-360. 

[11]

G. Cachon, Competitive supply chain inventory management, in Quantitative Models for Supply Chain Management, Kluwer, Boston, MA, 1998, 111–146. doi: 10.1007/978-1-4615-4949-9-5.

[12]

G. Cachon, Supply chain coordination with contracts, in Handbook in Operations Research and Management Science: Supply Chain Management, Elsevier Science Publishers, North Holland, The Netherlands, 2003, 227–339. doi: 10.1016/S0927-0507(03)11006-7.

[13]

G. Cachon and M. Lariviere, Contracting to assure supply: How to share demand forecasts in supply chain, Manage. Sci., 47 (2001), 629-646. 

[14]

J. ChenH. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583. 

[15]

C. Corbett and X. Groote, A supplier's optimal quantity discount policy under asymmetric information, Manage. Sci., 46 (2000), 444-450. 

[16]

C. CorbettD. Zhou and C. Tang, Designing supply contracts: Contract type and information asymmetry, Manage. Sci., 50 (2004), 550-559. 

[17]

A. Ha, Supplier-buyer contracting: Asymmetric cost information and cutoff policy for buyer participation, Nav. Res. Log., 48 (2001), 41-64. 

[18]

E. Inssa and F. Stroffolini, Price-cap regulation, revenue sharing and information acquisition, Inf. Econ. Policy, 17 (2005), 217-230. 

[19]

E. Inssa and F. Stroffolini, Price-cap regulation and information acquisition, Int. J. Ind. Organ., 20 (2002), 1013-1036. 

[20]

A. IozziJ. Poritz and E. Valentini, Socal preferences and price cap regualtion, J. Public Econ. Theory, 4 (2002), 95-114. 

[21]

J. KangD. Weisman and M. Zhang, Do consumers benefit from tighter price cap regulation?, Econ. Lett., 67 (2000), 113-119.  doi: 10.1016/S0165-1765(99)00252-9.

[22]

P. Law, Tighter average revenue regulation can reduce consumer welfare, J. Ind. Econ., 43 (1995), 399-404.  doi: 10.2307/2950551.

[23]

J. Laffont and D. Mortimort The Theory of Incentive: The Principal-Agent Model, Princeton University Press, Princeton, NJ, 2002.

[24]

J. Laffont and J. Rochet, Regulation of a risk averse firm, Game. Econ. Behav., 25 (1998), 149-173.  doi: 10.1006/game.1998.0639.

[25]

T. Lewis and C. Garmon, Fundamentals of Incentive Regulation, 12th PURC/World Bank International Training Program on Utility Regulation and Strategy, Gainesville, 2002.

[26]

C. Liston, Price cap versus rate of return regulation, J. Regul. Econ., 5 (1993), 25-48.  doi: 10.1007/BF01066312.

[27]

M. Lariviere, A note on probability distributions with increasing generalized failure rates, Oper. Res., 54 (2006), 602-604.  doi: 10.1287/opre.1060.0282.

[28]

R. Myerson, Incentive compatibiltiy and the bargaining problem, Econometrica, 47 (1979), 61-74.  doi: 10.2307/1912346.

[29]

Ö. Özer and W. Wei, Strategic commitment for optimal capacity decision under asymmetric forecast information, Manage. Sci., 52 (2006), 1238-1257. 

[30]

Ö. Özer and G. Raz, Supply chain sourcing under asymmetric information, Prod. Oper. Manag., 20 (2011), 92-115. 

[31]

J. Reitzes, Downstream price-cap regulation and upstream market power, J. Regul. Econ., 33 (2008), 179-200. 

[32]

D. Sappington and D. Weisman, Price cap regulation: What have we learned from 25 years of experience in the telecommunications industry?, J. Regul. Econ., 38 (2010), 227-257. 

[33]

Y. Shen and S. Willems, Coordinating a channel with asymmetric cost information and the manufactures' optimality, Int. J. Prod. Econ., 135 (2012), 125-135. 

[34]

D. Sibley, Asymmetric information, incentives and price cap regulation, Rand J. Econ., 20 (1989), 392-404.  doi: 10.2307/2555578.

[35]

G. Voigt and K. Inderfurth, Supply chain coordination and setup cost reduction in case of asymmetric information, OR Spectrum, 33 (2011), 99-122. 

Figure 1.  Information structure's impact on the optimal contract
Figure 2.  Price cap's impact on the optimal contract under full information
Figure 3.  Price cap's impact on the revenue under full information
Figure 4.  Price cap's impact on the optimal contract under private information
Figure 5.  Price cap's impact on the revenue under private information
Table 1.  Information structure's impact on contract
$Scenario$ $p$ $t$
$full$ $information$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
$private$ $information$ $x+8$ $-0.5x^{2}-x+63.3$
$Scenario$ $p$ $t$
$full$ $information$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
$private$ $information$ $x+8$ $-0.5x^{2}-x+63.3$
Table 2.  Price cap's impact on the optimal contact under full information
$Scenario$ $p^{**}$ $t^{**}$
$RPCR$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
$TPCR$ $16.75$ $-0.2x^{2}+3.25x+3.25$
$MPCR\,when\,x\geq x_{0}$ 17.75 $-0.2x^{2}+2.25x+2.25$
$MPCR\,when\, x < x_{0}$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
$Scenario$ $p^{**}$ $t^{**}$
$RPCR$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
$TPCR$ $16.75$ $-0.2x^{2}+3.25x+3.25$
$MPCR\,when\,x\geq x_{0}$ 17.75 $-0.2x^{2}+2.25x+2.25$
$MPCR\,when\, x < x_{0}$ $0.5x+13$ $-0.7x^{2}+6.5x+7$
Table 3.  Price cap's impact on the optimal contact under private information
$Scenario$ $p_{1}^{**}$ $t_{1}^{**}$
$RPCR$ $x+8$ $-0.5x^{2}-x+63.3$
$TPCR $ $16.75$ 16.3
$MPCR\, when\, x\geq x_{1}$ $17.75$ 5.175
$MPCR\,when\, x< x_{1}$ $x+8$ $-0.5x^{2}-x+63.3$
$Scenario$ $p_{1}^{**}$ $t_{1}^{**}$
$RPCR$ $x+8$ $-0.5x^{2}-x+63.3$
$TPCR $ $16.75$ 16.3
$MPCR\, when\, x\geq x_{1}$ $17.75$ 5.175
$MPCR\,when\, x< x_{1}$ $x+8$ $-0.5x^{2}-x+63.3$
Table 4.  Price cap's impacts on the downstream monopolist's profit, the consumers' surplus and the social total welfare under full information
$Scenario$ $U^{**}$ $S^{**}$ $W^{**}$
$RPCR$ $0.45x^{2}\!-\!7x+49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$
$TPCR$ $0.2x^{2}\!-\!3.25x\!+\!34.94$ $5.28$ $0.2x^{2}\!-\!3.25x\!+\!40.22$
$MPCR\,when\,x\geq x_{0}$ $0.2x^{2}\!-\!2.25x\!+\!26.44$ $2.53$ $0.2x^{2}\!-\!2.25x\!+\!28.97$
$MPCR\,when\, x < x_{0}$ $0.45x^{2}\!-\!7x\!+\!49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$
$Scenario$ $U^{**}$ $S^{**}$ $W^{**}$
$RPCR$ $0.45x^{2}\!-\!7x+49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$
$TPCR$ $0.2x^{2}\!-\!3.25x\!+\!34.94$ $5.28$ $0.2x^{2}\!-\!3.25x\!+\!40.22$
$MPCR\,when\,x\geq x_{0}$ $0.2x^{2}\!-\!2.25x\!+\!26.44$ $2.53$ $0.2x^{2}\!-\!2.25x\!+\!28.97$
$MPCR\,when\, x < x_{0}$ $0.45x^{2}\!-\!7x\!+\!49$ $0.125x^{2}\!-\!3.5x\!+\!24.5$ $0.575x^{2}\!-\!10.5x\!+\!73.5$
Table 5.  Price cap's impacts on the downstream monopolist's profit, the upstream monopolist's profit, the consumers surplus and the social total welfare under private information
$Scenario$ $U_{1}^{**}$ $\pi_{1}^{**}$ $S_{1}^{**}$ $W_{1}^{**}$
$RPCR$ $22.53$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.83$
$TPCR$ $21.89$ $0.2x^{2}\!-\!3.25x\!+\!13.05$ $5.28$ $0.2x^{2}\!-\!3,25x\!+\!40.22$
$MPCR\,when\, x\geq x_{1}$ $22.52$ $0.2x^{2}\!-\!2.25x\!+\!2.93$ 2.53 $0.2x^{2}\!-\!2,25x\!+\!27.98$
$MPCR\,when\, x < x_{1}$ $22.52$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.82$
$Scenario$ $U_{1}^{**}$ $\pi_{1}^{**}$ $S_{1}^{**}$ $W_{1}^{**}$
$RPCR$ $22.53$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.83$
$TPCR$ $21.89$ $0.2x^{2}\!-\!3.25x\!+\!13.05$ $5.28$ $0.2x^{2}\!-\!3,25x\!+\!40.22$
$MPCR\,when\, x\geq x_{1}$ $22.52$ $0.2x^{2}\!-\!2.25x\!+\!2.93$ 2.53 $0.2x^{2}\!-\!2,25x\!+\!27.98$
$MPCR\,when\, x < x_{1}$ $22.52$ $0.7x^{2}\!-\!12x\!+\!51.3$ $0.5x^{2}\!-\!12x\!+\!72$ $1.2x^{2}\!-\!24x\!+\!145.82$
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